Study on Multivariable Decoupling Control of Small PWR Pressurizer based on Active Disturbance Rejection Control
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摘要: 小型压水堆稳压器具有非线性、时变和强耦合等特点，很难建立准确的数学模型，传统控制方法难以取得满意的控制效果。因此提出了一种基于自抗扰技术（ADRC）的稳压器多变量解耦控制方法。首先搭建稳压器三区非平衡模型，基于微小摄动理论对模型进行线性化处理，得到压力和水位耦合传递函数方程。然后，基于传递函数设计稳压器ADRC解耦控制器，使用差分进化算法对控制器参数进行多目标优化。最后，以小型堆稳压器为研究对象，利用MATLAB仿真平台将ADRC解耦控制与传统比例-积分-微分（PID）控制进行对比分析。结果表明，所设计的控制器能够有效解决稳压器压力和水位之间的耦合问题，较传统PID控制器具备更好的抗干扰性和鲁棒性，为ADRC方法在稳压器的工程应用提供了理论基础。
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关键词:
- 稳压器 /
- 三区非平衡模型 /
- 自抗扰技术（ADRC） /
- 解耦控制
Abstract: Since the pressurizer (PZR) in a small pressurized water reactor (PWR) features non-linearity, time-dependence, and strong coupling, its accurate mathematical model is hard to build and the traditional control method cannot provide a satisfactory control effect. Therefore, this study describes a multivariable decoupling control method based on the active disturbance rejection control (ADRC) technique for such PZR. In this study, a non-equilibrium three-region model of PZR is built, and processed linearly based on the perturbation theory to generate the pressure and water level coupled transfer function equation. Then, an ADRC based decoupling controller is designed based on the transfer function, and the parameters of the controller are subjected to multi-objective optimization via differential evolution. Finally, the ADRC based decoupling control and traditional proportional-integral-derivative (PID) control for the same small reactor PZR are compared and analyzed by the MATLAB simulation platform. As demonstrate by the comparison, the ADRC based decoupling controller can effectively solve the PZR pressure and level coupling problem and has better robustness and interference immunity than the traditional PID controller. Therefore, this study provides a theoretical foundation for the engineering application of the ADRC method to the PZRs.-
Key words:
- PZR /
- Non-equilibrium three-region model /
- ADRC /
- Decoupling control
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图 1 稳压器模型示意图
Qh—电加热器功率；Wsp—喷淋流量；Wwc—壁面蒸汽凝结流量；Wsc—喷淋冷凝流量；Wfl—闪蒸流量；Wb—汽泡上升流量；Wsu—波动流量；Wro—汽液界面蒸汽过冷凝结流量
Figure 1. Schematic Diagram of PZR Model
图 2 二阶ADRC控制系统框图
v—设定值信号；v1—跟踪信号；v2—跟踪微分信号；z1—输出信号（y）的估计值；z2—变化速度估计值；z3—扰动量估计值；u—被控对象输入信号；e1—跟踪偏差；e2—跟踪微分偏差；b0—补偿因子；u0—NLSEF计算输出信号
Figure 2. Diagram of Second-Order ADRC Based Controller
图 3 稳压器系统结构图
G11、G21、G34—Qh、$W_{{\rm{su}}}^ + $和$W_{{\rm{su}}}^ - $对压力的传递函数；G12、G22、G44—Qh、$W_{{\rm{su}}}^ + $和$W_{{\rm{su}}}^ - $对水位的传递函数；u1、u2—压力和水位控制器输出
Figure 3. Structure Diagram of PZR System
图 4 稳压器ADRC解耦控制系统
Pset—压力设定值；Lset—水位设定值；G(s)—稳压器传递函数模型；ADRC1—压力控制器；ADRC2—水位控制器
Figure 4. Diagram of ADRC Based Decoupling Controller of PZR
图 8 波动流量扰动下的稳压器压力响应曲线
Figure 8. PZR Pressure Response Curve under Fluctuating Flow Disturbance
图 9 波动流量扰动下的稳压器水位响应曲线
Figure 9. PZR Level Response Curve under Fluctuating Flow Disturbance
图 10 不同K11时稳压器压力响应曲线
Figure 10. PZR Pressure Response Curve Corresponding to Different K11 Values
图 11 不同K11时稳压器水位响应曲线
Figure 11. PZR Level Response Curve Corresponding to Different K11 Values
表 1 稳压器主要参数
Table 1. Main Parameters of PZR
物理量名称 数值 运行压力/MPa 15.5 冷却剂平均温度/℃ 310 饱和水（汽）温度/℃ 344.76 饱和水密度/(kg·m−3) 594.53 饱和汽密度/(kg·m−3) 101.93 主冷却剂体积/m3 58.5 稳压器体积/m3 13.5 
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